Problem 2 For wavelengths in the visible spectrum, the index of refraction of a cer- tain type of crown glass can be approximated by the relation n(^) = 1.5255 + (4825 nm²)/x². b. Find the phase velocity, in this glass, for a pulse with frequency com- ponents centered around 500 nm. c. Find the group velocity, in this glass, for a pulse with frequency com- ponents centered around 500 nm.
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- Consider the geometry shown in the figure. The upper right quadrant is filled with a medium with a refractive index V3 and the rest of space is vacuum. A plane wave is n2 = incident on the xy plane from the left with an incident angle "1 = of 60 degrees. Its electric field is linearly polarized along the y direction. Find the power reflection and transmission coeffi- cients at the ryY plane and at the yz plane, respectively. What if the electric field is polarized in the xz plane? n2 = V3 y O1. Based on the material properties shown in the table, draw and explain electric field distribution assuming AC (60 Hz) voltage. (clearly show the difference in refraction angle) U Material 1 E (Vacuum Permittivity) Er (Relative Permittivity) Y (Conductivity) d (Thickness) Material 1 Material 2 8.85 x 10-12 [F/m] 1 10-15 [S/m] 3 10-18 [S/m] 5 [mm] 1 [mm] Dielectric Strength U (Voltage) 3 [kV/mm] 40 [kV/mm] 20 [kV] Material 2 2. Based on the material properties shown in the table, draw and explain electric field distribution assuming DC (0 Hz) voltage. (clearly show the difference in refraction angle) U Material 1 Material 2Consider a fiber like the one sketched below. Take the index of refraction of the core to be n₁ = 1.52 and the index of refraction of the cladding to be n₂ = 1.46. A) What is the critical angle for the core/cladding interface? B) If the input angle from air is 00= 10° Calculate 01. C) If the input angle from air is 80-10° Calculate y. D) If the input angle from air is 00=10° will the ray be guided by the fiber with low loss? E) If the input angle from air is 00=30° Calculate 0₁. F) If the input angle from air is 00=30° Calculate y. G) If the input angle from air is 00=30° will the ray be guided by the fiber with low loss? H) What is the maximum input angle from air for a ray that will be guided with low loss by this fiber?
- 2. In linear and circular polarization, consider monochromatic plane waves with frequency w propagating along the z axis in a dielectric characterized by permeabilities &, µ. a) Construct all linearly polarized wave and circular polarized wave solutions. Calculate E and B, given that Ex = Bx = 240 b) Consider two linearly polarized waves with E ||x and E ||y, respectively. Under what conditions their superposition is characterized by (i)linear and (ii) circular polarization? Given that Ex = 240You are in a room lit only by blue light. A chair in that room looks black to you. (Your eyes see red + green light as yellow; your eyes see red+ blue light as magenta; your eyes see green and blue light as cyan) a. What colors of light is the chair reflecting in the blue room? What colors of light is the chair absorbing in that room? Explain. b. You then move the chair out into the sunlight. What possible colors could the chair be in the sunlight? Explain.Please draw the scattering configuration